Problem: If $g(x) = 2x^2+2x-1$, what is the value of $g(g(2))$?
We have $g(2) = 2(2^2) + 2(2) - 1 = 8+4-1=11$, so \[g(g(2)) = g(11) = 2(11)^2 +2(11) -1 = 242 +22 -1 =\boxed{263}.\]